Solve 36x/9x^2*12x^7/2x*5/x^2

$$\frac { 36 x } { 9 x ^ { 2 } } \times \frac { 12 x ^ { 7 } } { 2 x } \times \frac { 5 } { x ^ { 2 } }$$

Evaluate

$$120x^{3}$$

Solution Steps

Cancel out 9x in both numerator and denominator.

$$\frac{4}{x}\times \frac{12x^{7}}{2x}\times \frac{5}{x^{2}}$$

Cancel out 2x in both numerator and denominator.

$$\frac{4}{x}\times 6x^{6}\times \frac{5}{x^{2}}$$

Express \frac{4}{x}\times 6 as a single fraction.

$$\frac{4\times 6}{x}x^{6}\times \frac{5}{x^{2}}$$

Express \frac{4\times 6}{x}x^{6} as a single fraction.

$$\frac{4\times 6x^{6}}{x}\times \frac{5}{x^{2}}$$

Cancel out x in both numerator and denominator.

$$4\times 6x^{5}\times \frac{5}{x^{2}}$$

Express 4\times 6x^{5}\times \frac{5}{x^{2}} as a single fraction.

$$\frac{4\times 6x^{5}\times 5}{x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$4\times 5\times 6x^{3}$$

Multiply 4 and 5 to get 20.

$$20\times 6x^{3}$$

Multiply 20 and 6 to get 120.

$$120x^{3}$$

Differentiate w.r.t. x

$$360x^{2}$$

Steps Using Definition of a Derivative

Cancel out 9x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{x}\times \frac{12x^{7}}{2x}\times \frac{5}{x^{2}})$$

Cancel out 2x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{x}\times 6x^{6}\times \frac{5}{x^{2}})$$

Express \frac{4}{x}\times 6 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 6}{x}x^{6}\times \frac{5}{x^{2}})$$

Express \frac{4\times 6}{x}x^{6} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 6x^{6}}{x}\times \frac{5}{x^{2}})$$

Cancel out x in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4\times 6x^{5}\times \frac{5}{x^{2}})$$

Express 4\times 6x^{5}\times \frac{5}{x^{2}} as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4\times 6x^{5}\times 5}{x^{2}})$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4\times 5\times 6x^{3})$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20\times 6x^{3})$$

Multiply 20 and 6 to get 120.

$$\frac{\mathrm{d}}{\mathrm{d}x}(120x^{3})$$

The derivative of ax^{n} is nax^{n-1}.

$$3\times 120x^{3-1}$$

Multiply 3 times 120.

$$360x^{3-1}$$

Subtract 1 from 3.

$$360x^{2}$$